Chapter 9, Problem 27PS

(a)

Interpretation Introduction

Interpretation:

The electronic configuration in molecular orbital term should be written for the given molecule chlorine monoxide $ClO$

Concept Introduction:

Molecular orbital (MO) theory:  is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule.

According to this theory there are two types of orbitals,

1. (1) Bonding orbitals
2. (2) Antibonding orbitals

Electrons in molecules are filled in accordance with the energy; the anti-bonding orbital has more energy than the bonding orbitals.

The electronic configuration of oxygen molecule $O_2$ can be represented as follows,

${\left({\text{σ}}_{\text{1s}}\right)}^2{\left({\text{σ*}}_{\text{1s}}\right)}^2{\left({\text{σ}}_{\text{2s}}\right)}^2{\left({\text{σ*}}_{\text{2s}}\right)}^2{\left({\text{σ}}_{\text{2p}}\right)}^2{\left( {\pi }_{\text{2p}}\right)}^4{\left( \pi {*}_{\text{2p}}\right)}^2$

The * represent the antibonding orbital

Answer to Problem 27PS

The electronic configuration $ClO$ molecule is,

${\left({\text{σ}}_{\text{2s}}\right)}^2{\left({\text{σ*}}_{\text{2s}}\right)}^2{\left( {\pi }_{\text{2p}}\right)}^4{\left({\text{σ}}_{\text{2p}}\right)}^2 {\left( \pi {*}_{\text{2p}}\right)}^3$

Explanation of Solution

There are $13$ valence electrons in $ClO$ molecule.

In accordance with the MO theory, the electron configuration of this molecule can be written as follows,

${\left({\text{σ}}_{\text{2s}}\right)}^2{\left({\text{σ*}}_{\text{2s}}\right)}^2{\left( {\pi }_{\text{2p}}\right)}^4{\left({\text{σ}}_{\text{2p}}\right)}^2 {\left( \pi {*}_{\text{2p}}\right)}^3$

(b)

Interpretation Introduction

Interpretation:

The Highest Occupied Molecular Orbital (HOMO) in the given molecule chlorine monoxide $ClO$ should be determined.

Concept Introduction:

Molecular orbital (MO) theory:  is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule.

According to this theory there are two types of orbitals,

1. (1) Bonding orbitals
2. (2) Antibonding orbitals

Electrons in molecules are filled in accordance with the energy; the anti-bonding orbital has more energy than the bonding orbitals.

The electronic configuration of oxygen molecule $O_2$ can be represented as follows,

${\left({\text{σ}}_{\text{1s}}\right)}^2{\left({\text{σ*}}_{\text{1s}}\right)}^2{\left({\text{σ}}_{\text{2s}}\right)}^2{\left({\text{σ*}}_{\text{2s}}\right)}^2{\left({\text{σ}}_{\text{2p}}\right)}^2{\left( {\pi }_{\text{2p}}\right)}^4{\left( \pi {*}_{\text{2p}}\right)}^2$

The * represent the antibonding orbital

HOMO and LUMO: This terms are stands for highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), respectively. So this energy difference between the HOMO and LUMO is termed the HOMO–LUMO gap.

Answer to Problem 27PS

The $\left( \pi {*}_{\text{2p}}\right)$ electron is the highest occupied molecular orbital.

Explanation of Solution

There are $13$ valence electrons in $ClO$ molecule.

In accordance with the MO theory, the electron configuration of this molecule can be written as follows,

${\left({\text{σ}}_{\text{2s}}\right)}^2{\left({\text{σ*}}_{\text{2s}}\right)}^2{\left( {\pi }_{\text{2p}}\right)}^4{\left({\text{σ}}_{\text{2p}}\right)}^2 {\left( \pi {*}_{\text{2p}}\right)}^3$

The molecular Orbital diagram for the given molecule can be drawn as follows,

  $\begin{array}{l}\text{σ*2p}\\ --\boxed{}--\to (\text{Anti}\text{bonding}\text{electrons})\\ \\ --\boxed{\uparrow \downarrow }-\boxed{\uparrow }--\\ {\text{π*}}_{\text{2p}}{\text{π*}}_{\text{2p}}\\ \\ --\boxed{\uparrow \downarrow }-\boxed{\uparrow \downarrow }-\boxed{\uparrow }----\boxed{\uparrow \downarrow }-\boxed{\uparrow }-\boxed{\uparrow }--\\ {\text{2}}_{\text{px}}{\text{2}}_{\text{py}}{\text{2}}_{\text{pz}}{\text{2}}_{\text{px}}{\text{2}}_{\text{py}}{\text{2}}_{\text{pz}}\\ \\ \\ {\text{σ}}_{\text{2p}}\\ --\boxed{\uparrow \downarrow }--\to (\text{Bonding}\text{electrons})\\ \\ --\boxed{\uparrow \downarrow }-\boxed{\uparrow \downarrow }--\\ {\text{π}}_{\text{2p}}{\text{π}}_{\text{2p}}\end{array}$

                            $\begin{array}{l}\\ --\boxed{\uparrow \downarrow }--\to (\text{Anti}\text{bonding}\text{electrons})\\ \left(\sigma *2s\right)\\ \\ --\boxed{\uparrow \downarrow }----\boxed{\uparrow \downarrow }--\\ 2s2s\\ \\ --\boxed{\uparrow \downarrow }--\to (\text{Bonding}\text{electrons})\\ {\left(\sigma 2s\right)}^2\end{array}$

    $\begin{array}{l}\\ --\boxed{\uparrow \downarrow }--\to (\text{Anti}\text{bonding}\text{electrons})\\ \left(\sigma *2s\right)\\ \\ --\boxed{\uparrow \downarrow }----\boxed{\uparrow \downarrow }--\\ 2s2s\\ \\ --\boxed{\uparrow \downarrow }--\to (\text{Bonding}\text{electrons})\\ {\left(\sigma 2s\right)}^2\end{array}$

In the ($ClO$) molecule, three electrons were occupied in p-orbitals mainly in $\left( \pi {*}_{\text{2p}}\right)$ molecular orbital. Therefore, it is the highest occupied molecular orbital.

(c)

Interpretation Introduction

Interpretation:

It should be checked that whether the given molecule is diamagnetic or paramagnetic in nature.

Concept Introduction:

Molecular orbital (MO) theory:  is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule.

According to this theory there are two types of orbitals,

1. (1) Bonding orbitals
2. (2) Antibonding orbitals

Electrons in molecules are filled in accordance with the energy; the anti-bonding orbital has more energy than the bonding orbitals.

The electronic configuration of oxygen molecule $O_2$ can be represented as follows,

${\left({\text{σ}}_{\text{1s}}\right)}^2{\left({\text{σ*}}_{\text{1s}}\right)}^2{\left({\text{σ}}_{\text{2s}}\right)}^2{\left({\text{σ*}}_{\text{2s}}\right)}^2{\left({\text{σ}}_{\text{2p}}\right)}^2{\left( {\pi }_{\text{2p}}\right)}^4{\left( \pi {*}_{\text{2p}}\right)}^2$

The * represent the antibonding orbital

Atoms with unpaired electrons are called Paramagnetic. Paramagnetic atoms are attracted to a magnet.

Atoms with paired electrons are called diamagnetic. Diamagnetic atoms are repelled by  a magnet

Answer to Problem 27PS

The given molecule $ClO$ is paramagnetic in nature.

Explanation of Solution

There are $13$ valence electrons in $ClO$ molecule.

In accordance with the MO theory, the electron configuration of this molecule can be written as follows,

${\left({\text{σ}}_{\text{2s}}\right)}^2{\left({\text{σ*}}_{\text{2s}}\right)}^2{\left( {\pi }_{\text{2p}}\right)}^4{\left({\text{σ}}_{\text{2p}}\right)}^2 {\left( \pi {*}_{\text{2p}}\right)}^3$

The molecular Orbital diagram for the given molecule can be  drawn  as follows,

  $\begin{array}{l}\text{σ*2p}\\ --\boxed{}--\to (\text{Anti}\text{bonding}\text{electrons})\\ \\ --\boxed{\uparrow \downarrow }-\boxed{\uparrow }--\\ {\text{π*}}_{\text{2p}}{\text{π*}}_{\text{2p}}\\ \\ --\boxed{\uparrow \downarrow }-\boxed{\uparrow \downarrow }-\boxed{\uparrow }----\boxed{\uparrow \downarrow }-\boxed{\uparrow }-\boxed{\uparrow }--\\ {\text{2}}_{\text{px}}{\text{2}}_{\text{py}}{\text{2}}_{\text{pz}}{\text{2}}_{\text{px}}{\text{2}}_{\text{py}}{\text{2}}_{\text{pz}}\\ \\ \\ {\text{σ}}_{\text{2p}}\\ --\boxed{\uparrow \downarrow }--\to (\text{Bonding}\text{electrons})\\ \\ --\boxed{\uparrow \downarrow }-\boxed{\uparrow \downarrow }--\\ {\text{π}}_{\text{2p}}{\text{π}}_{\text{2p}}\end{array}$

                            $\begin{array}{l}\\ --\boxed{\uparrow \downarrow }--\to (\text{Anti}\text{bonding}\text{electrons})\\ \left(\sigma *2s\right)\\ \\ --\boxed{\uparrow \downarrow }----\boxed{\uparrow \downarrow }--\\ 2s2s\\ \\ --\boxed{\uparrow \downarrow }--\to (\text{Bonding}\text{electrons})\\ {\left(\sigma 2s\right)}^2\end{array}$

    $\begin{array}{l}\\ --\boxed{\uparrow \downarrow }--\to (\text{Anti}\text{bonding}\text{electrons})\\ \left(\sigma *2s\right)\\ \\ --\boxed{\uparrow \downarrow }----\boxed{\uparrow \downarrow }--\\ 2s2s\\ \\ --\boxed{\uparrow \downarrow }--\to (\text{Bonding}\text{electrons})\\ {\left(\sigma 2s\right)}^2\end{array}$

In the ($ClO$) molecule, there is one unpaired electron on the upper portion of the MO diagram.

Presence of an unpaired electron induces paramagnetic character to the molecule.

Therefore, the given molecule is paramagnetic in nature.

(d)

Interpretation Introduction

Interpretation:

Bond order and net $\sigma and\pi bonds$ in the given molecule should be determined.

Concept Introduction:

Molecular orbital (MO) theory:  is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule.

According to this theory there are two types of orbitals,

1. (1) Bonding orbitals
2. (2) Antibonding orbitals

Electrons in molecules are filled in accordance with the energy; the anti-bonding orbital has more energy than the bonding orbitals.

The electronic configuration of oxygen molecule $O_2$ can be represented as follows,

${\left({\text{σ}}_{\text{1s}}\right)}^2{\left({\text{σ*}}_{\text{1s}}\right)}^2{\left({\text{σ}}_{\text{2s}}\right)}^2{\left({\text{σ*}}_{\text{2s}}\right)}^2{\left({\text{σ}}_{\text{2p}}\right)}^2{\left( {\pi }_{\text{2p}}\right)}^4{\left( \pi {*}_{\text{2p}}\right)}^2$

The * represent the antibonding orbital

Bond order: It is the measure of number of electron pairs shared between two atoms.

$\text{Bond}\text{order}\text{=}\frac{\text{1}}{\text{2}}\left(\begin{array}{l}\text{Number}\text{of}\text{electrons}\text{in}\text{bondoing}\text{MOs-}\\ \text{Number}\text{of}\text{electrons}\text{in}\text{antibonding}\text{MOs}\end{array}\right)$

Explanation of Solution

There are $13$ valence electrons in $ClO$ molecule.

In accordance with the MO theory, the electron configuration of this molecule can be written as follows,

${\left({\text{σ}}_{\text{2s}}\right)}^2{\left({\text{σ*}}_{\text{2s}}\right)}^2{\left( {\pi }_{\text{2p}}\right)}^4{\left({\text{σ}}_{\text{2p}}\right)}^2 {\left( \pi {*}_{\text{2p}}\right)}^3$

$\begin{array}{l}\text{The bond order of can}\text{be }\text{calculated}\text{as}\text{follows,}\\ \\ \text{Bond}\text{order}\text{=}\frac{\text{1}}{\text{2}}\left(\begin{array}{l}\text{Number}\text{of}\text{electrons}\text{in}\text{bondoing}\text{MOs-}\\ \text{Number}\text{of}\text{electrons}\text{in}\text{antibonding}\text{MOs}\end{array}\right)\\ \text{Bond}\text{order}\text{=}\frac{(8-5)}{\text{2}}=\frac{3}{\text{2}}=1.5\end{array}$

From the bond order value it is clear that, there are net $1\sigma bondand0.5\pi bonds$ in the molecule.